The intent of this project is to develop new and improve existing instrumentation and to develop new experimental and data analysis methods for the characterization of biological macromolecules and the study of their interactions. In the area of the analysis of the data from analytical ultracentrifugation, further refinements have been made in the major breakthrough achieved by the use of light intensity data rather than light absorbency data from the analytical ultracentrifuge. The intensity data is advantageous because of its superior statistical properties and its potential to provide better parameter estimates in ultracentrifugal analyses. The major contribution in this area has been the development of a particularly robust and statistically valid method for estimating weights to be used when fitting light intensity data by non-linear least-squares curve-fitting. An invited paper describing this method of estimated weights has been published in the prestigious series Methods in Enzymology. Experience with this methodology has revealed unpredictable sub-optimal results and also that it is still a rather time consuming and labor intensive method. Further statistical studies indicate that the error distribution of absorbance data, which is a logarithmically skewed Cauchy-type distribution, falls in the category of "fat-tailed" distributions, so called because of the relatively large distribution of deviations in the tails when compared to those in the central portion of the total distribution. Data with distributions of this type are better fit by L-1 robust regression. This method utilizes minimization of the sum of the absolute values of the deviations of the data points with the reciprocal of the standard error of each point as its weight. It has the further virtue of being singularly insensitive to data "outliers," when compared to non-linear least-squares regression. Since absorbance data from the analytical ultracentrifuge is in the form of the absorbance and its standard error as a function of radial position, L-1 fitting is singularly rapid and easy and has yielded such outstandingly superior results that it is now replacing other fitting techniques in this laboratory. We have also been able to develop algorithms for performing a balanced bootstrap procedure for the estimation of the standard errors of the fitting parameters obtained by L-1 regression. A compiled MATLAB program (RobustEquiFit 1.0) has been developed for these analyses and is available for free distribution. An invited manuscript describing this work is being submitted for publication in a book on analytical ultracentrifugation to be published by the Royal Society of Chemistry. While L-1 regression has proved to be useful for the fitting of thermodynamic data in the form of changes of free energy as a function of temperature, the bootstrap cannot be applied because too few data points are available to make this possible. We have developed a weighting procedure for least-squares fitting that makes it essentially the robust equivalent of L-1 regression, and since the mathematical model used is linear in the parameters, the standard error estimates returned by the Levenburg-Marquardt algorithm are valid. Further work is being done in this area. Further experience has been gained with the method of multi-wavelength analysis described in a previous annual report; this facilitates analysis of protein-protein and protein-nucleic acid interactions by having one or both reactants uniquely labeled with appropriate chromophores, thus permitting a more definitive observation of the behavior, both alone and associated, of these components in the analysis by mathematical modeling. This method has been utilized in Project 1 Z01 OD10039-07, "Physical Biochemistry of Macromolecules."